Pie charts are representations that make it easy to compare proportions: in particular, they allow quick identification of very large proportions and very small proportions. They are generally based on large sets of data.

The pie chart below summarises the average weekly expenditure by a sample of families on food and drink. The whole circle represents 100% of the expenditure. The circle is then divided into ‘segments’, and the area of each segment represents a fraction or pe

Author(s): The Open University

License information

Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Plans of houses and instructions for assembling shelves, etc., often come in the form of scale diagrams. Each length on the diagram represents a length relating to the real house, the real shelves, etc. Often a scale is given on the diagram so that you can see which length on the diagram represents a standard length, such as a metre, on the real object. This length always represents the same standard length, wherever it is on the diagram and in whatever direction.

Author(s): The Open University

License information

Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. When prompted after exercise 2.2 to watch the video for this unit, return to this page and watch the four clips below. After you've watched the clips, return to the workbook.

Click 'View document' to open the workbook (PDF, 1.0 MB).

Author(s): The Open University

License information

Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equation which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and have some familiarity with complex numbers.

The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook.

In some applications of vectors there is a need to move
backwards and forwards between geometric form and component form; we
deal here with how to achieve this.

To start with, we recall definitions of cosine and sine. If
P is a point on the unit circle, and the line segment
OP makes an angle θ measured anticlockwise
from the positive x-axis, then
cos θ is the x-coordinate of
P and sin θ is the
y-coordinate of P (

Author(s): The Open University

License information

Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share